Mutually Unbiased Bases and Trinary Operator Sets for N Qutrits

A complete orthonormal basis of N-qutrit unitary operators drawn from the Pauli Group consists of the identity and 9^N-1 traceless operators. The traceless ones partition into 3^N+1 maximally commuting subsets (MCS's) of 3^N-1 operators each, whose joint eigenbases are mutually unbiased. We prove that Pauli factor groups of order 3^N are isomorphic to all MCS's, and show how this result applies in specific cases. For two qutrits, the 80 traceless operators partition into 10 MCS's. We prove that 4 of the corresponding basis sets must be separable, while 6 must be totally entangled (and Bell-like). For three qutrits, 728 operators partition into 28 MCS's with less rigid structure allowing for the coexistence of separable, partially-entangled, and totally entangled (GHZ-like) bases. However, a minimum of 16 GHZ-like bases must occur. Every basis state is described by an N-digit trinary number consisting of the eigenvalues of N observables constructed from the corresponding MCS.Comment: LaTeX, 10 pages, 2 references adde

Characterization of Binary Constraint System Games

We consider a class of nonlocal games that are related to binary constraint systems (BCSs) in a manner similar to the games implicit in the work of Mermin [N.D. Mermin, "Simple unified form for the major no-hidden-variables theorems," Phys. Rev. Lett., 65(27):3373-3376, 1990], but generalized to n binary variables and m constraints. We show that, whenever there is a perfect entangled protocol for such a game, there exists a set of binary observables with commutations and products similar to those exhibited by Mermin. We also show how to derive upper bounds strictly below 1 for the the maximum entangled success probability of some BCS games. These results are partial progress towards a larger project to determine the computational complexity of deciding whether a given instance of a BCS game admits a perfect entangled strategy or not.Comment: Revised version corrects an error in the previous version of the proof of Theorem 1 that arises in the case of POVM measurement

Structural Relaxation and Frequency Dependent Specific Heat in a Supercooled Liquid

We have studied the relation between the structural relaxation and the frequency dependent thermal response or the specific heat, $c_p(\omega)$, in a supercooled liquid. The Mode Coupling Theory (MCT) results are used to obtain $c_p(\omega)$ corresponding to different wavevectors. Due to the two-step relaxation process present in the MCT, an extra peak, in addition to the low frequency peak, is predicted in specific heat at high frequency.Comment: 14 pages, 13 Figure

Bogomol'nyi equations for solitons in Maxwell-Chern-Simons gauge theories with the magnetic moment interaction term

Without assuming rotational invariance, we derive Bogomol'nyi equations for the solitons in the abelian Chern-Simons gauge theories with the anomalous magnetic moment interaction. We also evaluate the number of zero modes around a static soliton configuration.Comment: 9 pages, Revtex, SNUTP-94/6

Quantum Entanglement dependence on bifurcations and scars in non autonomous systems. The case of Quantum Kicked Top

Properties related to entanglement in quantum systems, are known to be associated with distinct properties of the corresponding classical systems, as for example stability, integrability and chaos. This means that the detailed topology, both local and global, of the classical phase space may reveal, or influence, the entangling power of the quantum system. As it has been shown in the literature, the bifurcation points, in autonomous dynamical systems, play a crucial role for the onset of entanglement. Similarly, the existence of scars among the quantum states seems to be a factor in the dynamics of entanglement. Here we study these issues for a non-autonomous system, the Quantum Kicked Top, as a collective model of a multi-qubit system. Using the bifurcation diagram of the corresponding classical limit (the Classical Kicked Top), we analyzed the pair-wise and the bi-partite entanglement of the qubits and their relation to scars, as a function of the critical parameter of the system. We found that the pair-wise entanglement and pair-wise negativity show a strong maximum precisely at the bifurcation points, while the bi-partite entanglement changes slope at these points. We have also investigated the connection between entanglement and the fixed points on the branch of the bifurcation diagram between the two first bifurcation points and we found that the entanglement measures take their extreme values precisely on these points. We conjecture that our results on this behaviour of entanglement is generic for many quantum systems with a non-linear classical analogue.Comment: 14 pages, 6 figures in separate ps files, submitted for publicatio

Degree of entanglement for two qubits

In this paper, we present a measure to quantify the degree of entanglement for two qubits in a pure state.Comment: 5 page

Tomography of fast-ion velocity-space distributions from synthetic CTS and FIDA measurements

We compute tomographies of 2D fast-ion velocity distribution functions from synthetic collective Thomson scattering (CTS) and fast-ion D-alpha (FIDA) 1D measurements using a new reconstruction prescription. Contradicting conventional wisdom we demonstrate that one single 1D CTS or FIDA view suffices to compute accurate tomographies of arbitrary 2D functions under idealized conditions. Under simulated experimental conditions, single-view tomographies do not resemble the original fast-ion velocity distribution functions but nevertheless show their coarsest features. For CTS or FIDA systems with many simultaneous views on the same measurement volume, the resemblance improves with the number of available views, even if the resolution in each view is varied inversely proportional to the number of views, so that the total number of measurements in all views is the same. With a realistic four-view system, tomographies of a beam ion velocity distribution function at ASDEX Upgrade reproduce the general shape of the function and the location of the maxima at full and half injection energy of the beam ions. By applying our method to real many-view CTS or FIDA measurements, one could determine tomographies of 2D fast-ion velocity distribution functions experimentally